RHOPE: LLM-AUGMENTED ADAPTIVE EXPERIMENTAL DESIGN WITH COMPLEX CONTEXTUAL INFORMATION

Experimental design allocates limited measurement effort across candidate treatments to learn their expected outcomes. Adaptive designs refine allocations as evidence accumulates, improving estimation and treatment selection. Contextual information can inform these decisions, but exploiting unstructured or high-dimensional context remains challenging. We use large language models (LLMs) to transform complex context into proxy outcomes and propose Residual-Horizon Optimization for Prediction-Powered Experimentation (RHOPE), a principled Bayesian adaptive experimentation framework that combines true outcomes with LLM-generated proxy outcomes and formulates finite-batch design as a posterior Markov decision process (MDP). Our methodology uses proxy outcomes in two ways: sample augmentation improves estimation precision, while observing proxies before each allocation decision provides advance information. Synthetic experiments and semi-synthetic experiments using Genomics of Drug Sensitivity in Cancer (GDSC) data suggest that estimation precision drives most gains, with smaller advance-information gains, and highlight the importance of proxy informativeness and moment-estimation accuracy.